2284
J. Phys. Chem. 1993,97, 2284-2288
Uptake of Gas-Phase Acetone by Water Surfaces S. X. Duan, J. T. Jayne,' and P. Davidovits Department of Chemistry, Merkert Chemistry Center, Boston College. Chestnut Hill, Massachusetts 02167
D. R. Worsnop,' M. S. Zabniser, and C. E. Kolb Aerodyne Research, Inc., Billerica, Massachusetts 01821 Received: August 21, 1992; In Final Form: November 3, 1992
The mass accommodation coefficient (a)for acetone on water has been measured as a function of temperature in the range 260-285 K. The experimental method employs a monodispersed train of fast-moving droplets (80-230 pm in diameter) in a low-pressure flow reactor. Droplet-trace gas interaction times are on the order of a few milliseconds. The mass accommodation coefficient has a negative temperature dependence and decreases from 0.066 to 0.013 over the above range. As with the previously studied alcohols, CY can be expressed in terms of an observed Gibbs free energy as a / ( l - a) = exp(-AG*,b,/RT), with m o b s = -12.7 kcal/mol and M o b s = -53.6 eu. The implications of these results for atmospheric chemistry are examined.
Introduction The mass accommodation coefficient (a),which is the probability that a molecule that strikes the liquid surface will enter into the bulk liquid, is a key parameter governing the transport of gas-phase molecules into liquids. In a previously published article,' we presented mass accommodation measurements as a function of temperature for a series of gas-phase alcoholsand related specieson water. Several unexpected features were noted in the results. Initially it had been our expectation that the mass accommodation coefficient would be inversely proportional to the size of the molecule. The results showed no such correlation. Furthermore, we had expected that molecules that bind more strongly to water might form a more tightly bound complex at the surface and therefore would exhibit a mass accommodation coefficient with a steeper negative temperature dependence. In fact, the oppositewas observed. The temperature dependence of a was steeper for less tightly bound species. We then developed a model that provides an explanation for the observations.2 Here we present results of uptake studies for gasphase acetone that further substantiate that uptake model. The implications of these results for atmospheric chemistry are also discussed. The mass accommodation coefficient is defined as number of molecules absorbed by the surface CY' (1) number of molecular collisions with the surface and it determines the maximum flux of gas into a liquid. In many circumstances, however, mass accommodation is not the limiting process for the gas uptake. Instead it may be controlled by other processes, the most important of which are gas-phase diffusion and Henry's law saturation. On short time scales the volume of liquid subject to Henry's law saturation is determined by liquid-phase diffusion. In a laboratory experiment subject to these limitations, the measured flux, J,into a surface is expressed in terms of an uptake coefficient, ymca,,as
Here n, is the density of the gas molecules and 2 is the average thermal velocity. The uptake coefficient is a convolution of all the processes that affect the rateof gas uptake. The experimental task is toseparate
' Present address: Departmentof Earth AtmosphereandPlanetaryScience, MIT, Cambridge, MA 02139.
these effects. We have developed a laboratory method, using fast-moving droplets, for measuring these processes in a way that allows control of the factors affecting the gas uptake. In previous publications3-*we have described our laboratory technique and have reported uptake studies for SOz, HzOz, alcohols, aldehydes, HN03, HCl, and N205 with water droplets and, for the latter three, also with sulfuric acid droplets. Here we will provide only a brief summary of the experimental method. The gas uptake coefficient is measured by passing a highly controlled train of droplets through a low-pressure flow reactor ( 6 2 9 Torr) that contains the tracegasspecies, in thiscaseacetone, entrained in a flowing carrier gas of water vapor and helium. This fast moving stream of small monodispersed (80-230 rm in diameter dependingon the run) is produced in a separate chamber by a vibrating orifice jet (diameter, 63 pm). The density (ne) of the trace gas is monitored as the surface area of the droplets passing through the flow tube is changed in a stepwise fashion. The density of the species is monitored downstream of the flow tube with a quadrupole mass spectrometer. A measured decrease in the trace gas signal (An,) resulting from an increase in the exposed droplet surface area corresponds to an uptake of the gas by the droplet surface. The uptake coefficient (ymeas) is obtained from the measured change in trace gas signal via eq 3 (see ref 4).
(3) Here F, is the carrier gas volume rate of flow (cm3 s-I) through thesystem, A4 is the change in the total droplet surface in contact with the trace gas, and n, and n i are the trace gas densities at the outlet of the flow tube (Le., ng = n i An,). An important aspect of the experimental techniqueis the careful control of all the conditions within the apparatus. Control of the water vapor pressure is especially important because the temperature of the droplets is determined by the partial pressure of H2O vapor in both the droplet generation chamber and the flow tube. Equilibrium between ambient water vapor and the droplet train temperature is reached in the droplet production chamber. The attainment of droplet temperature equilibrium is predicted theoretically and has been checked e~perimentally.~ Careful control of the vapor pressure ensures that the droplets neither grow nor evaporate in the reaction zone. The present experiments were done with the pressure of H20 in the reaction zone between 13 and 1.7 Torr. This corresponds to temperatures between IS and -13 OC, respectively. The lower temperatures below 0 OC
0022-36S4/93/2097-2284g04.00/0 Q 1993 American Chemical Society
+
Uptake of Gas-Phase Acetone
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2285
are obtained by evaporative cooling of the droplets, which are supercooled but not frozenS4 The transit time of the droplets through the reaction zone is short, on the order of a few milliseconds. The gas-droplet interaction time can be varied from 1.8 to 21 ms by selecting the gas inlet port and by altering the droplet velocity. These two methods of varying the contact were shown to be equivalent. The various factors affecting gas uptake have been discussed in previous publications. Here we will present only the factors particularly relevant to acetone uptake. In our treatment of the overall uptake we express the various processes involved in terms of dimensionless uptake coefficient^.^ The initial phase of the uptake is governed by the gas-phasediffusion to the liquid surface (Ydirf) and the mass accommodation coefficient a. Because of equilibrium considerations, evaporation of acetonedue to Henry’s law saturation in the near surface liquid layer must also be considered. The saturation of the liquid is taken into account by the coefficient ysOl.The expressions for the ycoefficients are obtained by extension of the treatment in Worsnop et ala7and Jayne et aL8 and references there in. The gas diffusion process is taken into account via Ydiff as 1 -=-
E4
Ydiff
8Dg
0.05
Acetone
-2
\
#
YSOl
0.03
Y
9
0.02
0
Acetone
0.03
0.00
0
CY
Ydiff
1
4
8
12
:3
18
Contact t i m e (ms)
Here DI is the liquid-phasediffusion coefficient. Here again we used the value measured for propanol. This value is DI = 0.012 exp(-2100/T) cm2 s-l? The overall uptake coefficient rmcas is given by Ymcas
4
Figure 1. Plot of ln(n,/n,l) versus PAA/4Fg for acetone. The slope of and equals 0.0102 h 0.0025. Droplet temperature Td the line is ymcas = 263 K. Gas-droplet contact time t = 10 ms.
1 /2
I + - + -1
3
(4)
4RTH
- =1-
2
1
cAA/Fg
‘)
E
0.04
E
Here dr is an effective orifice diameter (dr = 1.8.63 pm; see refs 1, 4) and D, is the diffusion coefficient of acetone in the background gas. This parameter is not available for acetone. We used the D, values for propanol, which is a molecule of similar size and structure. This cannot make a significant difference since, as will be seen, the effect of diffusion on the uptake of acetone is less than 10%. The binary diffusion coefficients at 273 K and 1 atm are 0.082 cm2 s-I in HzO and 0.38 cm2 s-I in He.* The saturation of the liquid is taken into account by
-=-(1
tI-
0.04 h h
Figure 2. Gas uptake coefficient as a function of gas-droplet contact time for acetone (Td = 263 K). 500 r
I
I
400
(6)
Ysol
300
Upon substitution this expression becomes \
200
d
In this expression t is the gas-droplet interaction time, and therefore ymashere (as well as in eq 3) represents the total integrated uptake during exposure time r (Le., from 0 to t ) . The applicabilityof eq 7 was demonstrated by Worsnop et 81.: where the first time-dependent SOz uptake results were presented.
ReSultS
&tuple Data. In Figure 1, we show a representative plot of trace gas uptake in the form ln(n,/n,l) as a function of EhA/4F6 for acetone at 263 K. The slope of the line in the figure is y m a r a The fitted line is forced through the origin. The product E A A / 4Fgwas varied by changingthe gas flow rates and the total droplet surface area change (L4). Each point in the figure is the average of at least ten area change cycles. The error bars represent one standard deviation from the mean in the experimental An,/n, value. The data in Figure 2 were obtained for gas-droplet contact time of approximately 10 ms. The time dependence of the uptake coefficient for acetone is shown in Figure 2, which is a plot at 263 K as a function of
100
n ” 0
1
2
3
4
5
t 1’2(ms,”2 Figure 3. 1/ymeaeplotted as a function of r1I2 for acetone at three temperatures (see eq 7). Theslopeof the lines yields thevalueof H(D1) and the intercept is ( l / a l/ydifl). A is Td = 284,O is Td = 275 K and O is Td 263 K.
+
gas-droplet contact time. The solid line is a best fit to the data points using eq 7. Such time dependence measurements were performed over the whole temperature range studied and are used to obtain the mass accommodation coefficient, a. In Figure 3 we plot l/ymas as a function of t 1 l Zfor three representative droplet temperatures, 284,275, and 263 K. (The 263 K data in this figure are simply a replot of the data in Figure 2.) As is seen in eqs 6 and 7, the plots in Figure 3 yield a linear function with a slope containing the quantity 1fHD1’I2and an intercept equal to 1/a+ 1/ydia. Gas-droplet contact time studies
Duan et al.
2286 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 I
0.15 I
l
IO0
I
Acetone
Acetone
3.8
3.4
Droplet Temp (K)
3.8
4.0
Figure 4. Temperature dependence of a for acetone.
1/T ( lov3 K-' ) Figure 5. Semi-log plot of a / ( l - a) versus 1/T for acetone (see eq 8).
TABLE I: Sample Data
The values for AH,,b,/R and ASoa/R are obtained from the slope and the intercept of the fitted line.
H(DI
PH20, PHs3
T
Torr
Torr
ymsas t, ms
263 275 284
2.2 5.6 10.4
5.4 3.7 3.4
0.0105 9.5 0.0046 9.5 0.0027 11.0
4,
M atm-I cm s-'/~ cm2 SKI 0.46 0.25 0.14
19.0 10.4 6.2
3
10
(Y
0.061 0.013 0.010
,
o-Zhou and M a D D e r -This 2
10
such as shown in Figure 3 were performed over the full temperature range. The parameter 1/ H D I obtained from these studies was then used to account for saturation. In Table I we show examples of our data processing. Column 1 lists the temperature of the droplets. Columns 2 and 3 show the pressures of water vapor and helium carrier gas in the reaction region. Columns 4 and 5 list experimentally measured y values and corresponding gas-droplet contact times. The values of 1/ H D 1 are listed in column 6. Column 7 lists the values of Dg used to correct the zero time intercept of 1/ymeas (eq 7 as plotted in Figure 3) to obtain the mass accommodation coefficient a listed in column 8. The gas diffusion correction is C208. The values of a obtained from the intercepts of plots such as shown in Figure 3 as well as from single uptake coefficient measurements corrected for saturation (eq 7) are plotted together as a function of temperature in Figure 4. It was shown in ref 1 that the mass accommodation coefficient can be expressed as
The parameter AG*ob,can be regarded as the Gibbs free energy of the transition state between gas-phase and aqueous-phase solvation. The mass accommodation measurements are then expressed in terms of eq 8 by plotting the ln[a/(l - a)]as a function of 1/T. The slope of such a plot is -AHob/R and the intercept is AS,b/R. Such a plot for acetone is shown in Figure 5. From this plot we obtain M o b s = -12.7 kcalfmol and A S o b s = -53.6 eu. Our experimental data can also be used to obtain Henry's law constant H . This parameter is calculated from the slopes of the lines in plots such as shown in Figure 3, with the known parameters in eq 5. Our values obtained in the temperature range 263-284 K merge smoothly with earlier measurements of Zhou and Mopperlo who obtained H by direct measurements of gas- and liquid-phase densities in the range 283-318 K. Our results together with theirs are plotted in Figure 6. Following the formalism of Zhou and Mopper we express H as log H (M/atm) = A + B/ T (9) The Zhou and Mopper data yield A = -4.05 and B = 1667 (see ref 11). Our data yield A = -5.81 and B = 2145. The best fit to both data yields A = 4 . 4 7 and B = 1770.
z 8n 0
a
10'
kp
3.0
3.2
3.4
3.8
3.8
4.0
1/T ( K-') Figure 6. Plot of Henry's law constant (H) for acetone as a function of 1/T: 0 data of Zhou and Moper;lo 0 this work.
TABLE Ik Measured Values of A& molecule acetone methanol ethanol 1-propanol 2-propanol tert-butyl alcohol Cl-ethanol Br-ethanol I-ethanol formic acid acetic acid HNOj ethylene glycol HzOz
AHo&, kcaltmol -12.7 -8.0 -11.0 -9.2 -9.9 -8.2 -1.3 -8.4 -8.2 -7.9 -8.1 -6.6 -5.3 -5.5
and AS& ASo&. cal/mol/K -53.7 -34.9 -46.2 40.9 43.0 -35.8 -32.3 -35.9 -34.4 -34.9 -34.9 -27.6 -24.5 -22.5
Discussion In ref 1 we presented results of uptake measurements for a series of gas-phase alcohols and related species. The mass accommodation coefficients measured in these studies were expressed in terms of AH0b and ASobas defined in eq 8. These parameters are reproduced in Table 11. As was noted in ref 1, several features are evident in the tabulated results. First, as stated in the introduction, M o band Sob do not depend on the size or shape of the molecule. This is clearly evident from a comparison of the results for methanol and tert-butyl alcohol. The hydrophobic component of the tert-butyl alcohol is significantly larger than that of the methanol, yet Mobs and so^ are the same for the two species. Furthermore, in our initial conceptualization of the uptake
Uptake of Gas-Phase Acetone
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2287
process we had expected that molecules that bind more strongly to water would form a more strongly bound complex at the surface with an associated larger M o b . This is not the case. Hydrogen peroxide is more strongly bound to water than methanol, yet the magnitude of its m o b s is significantly lower. In fact, the magnitudes of m o b s are ordered as diols < HN03< acids C halo ethanols < alkyl alcohols. This arrangement seems to be inversely proportional to the expected hydrogen-bonding ability of the species. Finally, there is apparently a direct relationship between M o b and a smaller mobis correlated with a smaller Mobs.
In ref 2 we presented a model for the nonreactive uptake of gas molecules by liquids. The model uses the concept that the interfacial surface of a liquid is a narrow rekion of a dense gaslike state within which nucleation is continually occurring. In this region, clusters that reach a critical size grow by condensation and merge with the nearby bulk liquid. The incoming gas molecule participates in this nucleation process. If this molecule becomes part of a critical sized cluster it is then incorporated into the bulk liquid via condensation growth. A quantitative formulation of this model leads to an expression for the mass accommodation coefficient on water, which provides an explanation for these observations and is in agreement with experimental measurements. The expression in terms of AH0b and s o b s is mobs
=
and
Here N* is the number size of the critical cluster, V,,,is the molar volume of the condensing liquid (in this case water), @ is the surface tension of the liquid, M is the molarity of the liquid (for water M = 55.5 mol/L), N,, is Avogadro’s number, a n d p is the pressure in the surface region where condensation clustering is occurring. The parameters AH, and AS, are the enthalpy and entropy of condensation obtained from the Gibbs free energy of condensation (AGc = AHc - T M , ) . Here AG, is not the usually tabulated standard free energy of condensation. Rather it is the free energy of transferring a mole of gas into liquid without volume change.I2J3 The formulation leading to eqs 10and 11 is discussed in ref 2; a value o f p = 0.17 atm was used to fit the experimental m o b s and M o b s to the equations. Substituting numerical values given there for the parameters in eqs 10 and 11 yields mob = s -10(N*
- 1) + 4.79(N*2/3 - 1)
(12)
Mobs= -30.7(N* - 1) As was noted earlier, the values of AHob and G o b s are systematically different for the various species. The more hydrophilic the species the smaller are the magnitudes of the values for both m o b s and S o b . Thus for acetone M o b s = -1 2.7 kcal/mol and S o b= -53.7 eu, where as for the species with two O H functional groups (HZ02 and ethylene glycol) typically M o b s = -5.5 kcal/mol and s o b s = -23 eu. These observations were explained with the following assumptions. For all species critical clustering leading to species uptake occurs in the same surface region corresponding to pressure p in eq 11. This is likely the region where the incoming species is stopped by collisions with the molecules in the interface region. Further, we assume that the factor determining the critical cluster number size ( W )is not necessarily the number of molecules in the cluster but rather the number of hydrogen-bonding sites. Therefore, hydrophilic functional groups of the accommodating molecule can collaborate in the formation of the cluster, thereby reducing the number of water molecules required to form a critical cluster.
TABLE III: Calculated Values for AH, and AS& Obtained via a s 10 and 11 N* Mobs kcal , mol-’ 1
1.5 1.7 2 2.4 2.5 2.6 2.7 2.8
0 -3.5 -5.0 -7.2 -9.9 -11.0 -11.7 -12.5 -13.3
S scal 0 mol-’ ~ , K-’
0 -1 5 -22 -3 1 4 3 4 6 4 9 -52 -55
To illustrate, let us assume that the number of hydrogenbonding sites required for a critical-sized cluster is 3. For a molecule that has only a single bonding site (comprised of a lone OH group, for example), two water molecules need to be added to form such a critical cluster. Further, we assume that for the molecules containing two OH groups, the required number of hydrogen-bonding sites in a critical-sized cluster is likewise 3. But in this case the clustering process has a head start. The three sites may be formed by the two OH groups in the molecule itself plus a single added hydrogen bonded water molecule. The species uptake is now governed by the thermodynamics of a N* = 2 cluster, since the formation of such a cluster automatically leads to the required three hydrogen bonding sites. In turn, as can be seen from eqs 10 and 11, this smaller N* is associated with lower magnitudes of M o b s and Likewise for other species, different functional groups within the molecule may contribute to a greater or lesser extent to the condensation process, reducing or increasing the number-size requirement on the chiral cluster. In this way of viewing the process, one would expect the extent of such a collaborative effect to depend on the hydrogen-bonding capabilities of the species. Thus N* (and correspondinglythe magnitudesof AH0band ASob) would decrease or increase with the hydrophilic or hydrophobic nature of the species, respectively. Selected values of W and the corresponding values of m o b s and s o b s are shown in Table 111. These values are obtained from the experimental results via eqs 10 and 11 as discussed in ref 2. As is seen from the listing in Table 11, acetone follows the expected pattern. Acetone is the least hydrophilic in the sequence and therefore requires the highest W with the correspondingly largest magnitude of M o b s and G o b s . We are tempted, albeit after the fact, to test the predictive aspects of the uptake model. We approach this by examining the effects of the =O and OH hydrophilic functional groups on W . Ethanol, ethylene glycol, and acetic acid all have the same number of carbon atoms and are therefore well suited to serve for the comparison. We note that from the point of view of the clustering process acetone with its single carbonyl (=O) functional group is analogous to acetic acid without the hydroxyl (OH). Therefore we would expect to obtain N* for acetone by simply subtracting the effect of OH from the W associated with acetic acid. First we determine the effect of O H by examining the difference in W for ethanol and ethylene glycol. Using eq 13,we obtain for ethanol, which has one OH, N* = 2.50 and for glycol, which has two OH groups, N* = 1.80. Therefore the effect of an added OH is to decrease N* by 0.70. Since for acetic acid W = 2.14, this way of looking a t the process yields for acetone N* = 2.14 + 0.70 = 2.84. This in turn via eqs 12 and 13 yields m o b s = -13.6 kcal/ mol and mobs = -56 eu, which is good agreement with the measured m o b s = -12.7 kcal/mol and s o b s = -54 eu. We note here that the values of the critical cluster size N* extracted from the measured m o b s and G o b s are to be considered approximate. As is true in many applications of critical cluster size nucleation theory in the limit of small clusters bulk liquid parameters (e.g., surface tension) are not rigorously valid. As isdiscussedinref2, thevalueofp(eq 1l), theonefittedparameter
2288 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 used toobtained thenumericalvaluesineqs 12and 13,isextremely sensitive to those bulk parameters. However, the relative values of N+ for different species provide an insight into the nature of the accommodation process.
Implications for Atmospheric Chemistry Acetone (CH3COCH3), the simplest ketone, is widespread in the troposphere. It is produced there primarily by degradation reactions of a variety of light non-methane organic compounds (LNMHC).I4 Henderson et al.I4 and Chatfield et al.Is report concentrations of acetone ranging from 20 ppb in the Florida Everglades,to 0.2-1.8 ppb in rural Pennsylvania,to approximately 500 ppt in the remote Atlantic troposphere. Since acetone is relatively stable, it is long-lived in the atmosphere and therefore it has been suggested that its atmospheric concentration and chemistry can help in the characterization of sources of LNMHC,l4,lS Previous cloud modeling studies by SchwartzI6 and Jacob” have shown that in tropospheric clouds (droplets in the 10-50pm size range), the uptake coefficient for gas-phase diffusion, Ydiff, is less than Therefore the mass accommodation cocfficient,a,is the rate-determining parameter for gas/droplet mass transport if its value is less than For larger values of a,gas-phase diffusion limits are rate of gas uptake. Our results show that, depending on droplet temperature, a may be as small as and therefore both a and rdiffmay affect gas uptake. However, the Henry’s law coefficient for acetone is small; at 273 K H 30 M/atm. Therefore, the fraction of acetone in cloud droplets is only lC3(HRT X liquid water content = 30 X 25 X 10-6 l e 3 ) . Thus, as was pointed out by Chatfield et al.,Is the capacity of cloud droplets to remove acetone from the atmosphere is insignificant. Still the authors note that theuptake of acetone by clouds could be greatly enhanced if there were a fast, possibly catalytic, reaction in solution that could destroy acetone. Such an additional uptake is tentatively suggested as a possible explanation for the discrepancy between calculated model winter profiles for acetone and observed meas~rements.’~
-
-
Duan et al. Should the uptake of acetone by cloud droplets turn out to be significant, then the modeling of this uptake will have to include the gas/liquid mass transport kinetics.
Acknowledgment. D.R.W. acknowledges the continuing scientific inspiration of Dudley Herschbach, to whom this issue is dedicated. Funding for this work was provided by the National Science Foundation Grant ATM-90-13073 and the US.Environmental Protection Agency Grant R-8 15469-01-0. References and Notes (1) Jayne, J. T.; Duan, S. X.;Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1991, 95, 6329. (2) Davidovits, P.; Jayne, J. T.; Duan, S. X.;Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1991, 95, 6337. (3) Gardner, J. A.; Watson, L. R.; Adewuyi, Y. G.; Davidovits, P.; Zahniser, M. S.; Worsnop, D. R.; Kolb, C. E. J . Geophys. Res. 1987, 92, 10887. (4) Worsnop,D.R.:Zahniser,M.S.;Kolb,C. E.;Gardner, J.A.; Watson, L. R.; Van Doren, J. M.; Jayne, J. T.; Davidovits, P. J . Phys. Chem. 1989, 93. 1159. (5) Jayne, J. T.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J. Phys. Chem. 1990, 94,6041. (6) Van Doren, J. M.; Watson, L. R.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1990, 94, 3265. (71 Watson. L. R.: Van Doren. J. M.: Davidovits. P.: Worsnon ..D. R.: Zahniser, M. S.; Kolb,.C. E. J . Geophys. Res. 1990, 95, 5631. (8) Jayne, J. T.; Duan, S.X.;Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1992, 96, 5452. (9) Longsworth, L.G. Diffusion in Liquids. In American Institute of Physics Handbook, 3rd ed., McGraw Hill: New York, 1972; pp 221-229. (10) Zhou, X.;Mopper, K. Emiron. Sci. Technol. 1990, 24, 1864. (1 1) The values for these parameters quoted in the publication of Zhou and Mopper are somewhat different. In that publication they are given as A = -5.00 and B = 1977. The parameters we used were obtained by a plot of the Zhou and Mopper data quoted in the text. (12) Ben-Naim, A.; Marcus, Y . J . Chem. Phys. 1984, 25, 2016. ( 13) Ben-Naim, A. Soloation Thermodynamics;Plenum Press: New York, 1988. (14) Henders0n.G. C.; McConnell, J. C.; Evans, W. F. J. J . Atmos. Chem. 1989, 8, 277. (15) Chatfield, R . B.; Gardner, E. P.; Calvert, J. C.J. Geophys. Res. 1987, 92,42086. (16) Schwartz, S. E. J . Geophys. Res. 1984, 89, 11 589. (17) Jacob, D. J. J . Geophys. Res. 1986, 92, 9807.
